Question

Pleaseeee answer quick WILLL GIVE BRAINLIEST!!!!!! Given the expression: 5x10 − 80x2 Part A: Rewrite the expression by factoring out the greatest common factor. (4 points) Part B:Factor the entire expression completely. Show the steps of your work. (6 points)

Answer 1

Answer:

$5\,x^{10}-80\,x^2=5\,x^2\,(x^4+4)(x^2-2)(x^2+2)$

Step-by-step explanation:

First, extract the greatest common factor of the numerical as well as the variable parts:

the GCF of 5 and 80 is "5", and the GCF between $x^{10}$and $x^2$ is  $x^2$ , then:

$5\,x^{10}-80\,x^2=5\,x^2\,(x^8-16)$

Now, we can re-write the binomial in parenthesis as a difference o squares to be able to factor out even further:

$x^8-16=(x^4)^2-4^2=(x^4-4)(x^4+4)$

we now repeat the process for the binomial difference:

$(x^4-4)=((x^2)^2-2^2)=(x^2-2)(x^2+2)$

So finally the complete factorization is:

$5\,x^{10}-80\,x^2=5\,x^2\,(x^4+4)(x^2-2)(x^2+2)$